Monday, October 19, 2015

Interest rate dynamics!

John Cochrane has a new working paper where he looks at interest rate dynamics. I thought I'd do some simulations with the information equilibrium model -- in particular the DSGE form of it. First, as noticed by Ken Duda in comments at Cochrane's post (and Cochrane cedes), we don't really have an interest rate peg in the US today. In fact, I think pegged interest rates are important to whether or not interest rate targets can generate inflation (see here and here). It's actually fairly obvious in the (short term) interest rate data when rates were pegged and when they weren't:

With that out of the way, let's get to the results of the simulation. I looked at the effect of increasing the monetary base on (nominal) output, inflation and (nominal) interest rates using the DSGE form of the IT model. That means that we're taking the IT index k = 1/ κ to be constant. Therefore we're neglecting the impact of a changing index, which is the primary reason interest rates start off rising with the monetary base, but then start to fall with the inflection point some time in the 1980s. I normalized all the values to 1 at the first time step t = 1. And one last thing -- I took the nominal shocks (σ at the DSGE form link) to be zero.

Here's what happens when k is 'large' (or κ is 'small') as it was before the 1980s:

Expanding the base causes interest rates, output and inflation to rise. The rise in inflation is proportional to the rise in the base -- recall log P ~ (k - 1) log M. And output rises more than inflation -- expansionary monetary policy causes economic expansion. When k > 1, there is a tendency for k to fall since the increase of log n is smaller than the increase of log m if n > m. Which leads us to our next scenario.

When  is near 1 (meaning κ is near 1), like the situation in the US today, we have the following behavior:

Monetary expansion leads to lower interest rates and only a small amount of inflation and output. This is not quite the neo-Fisherite result since we still have inflation. In fact, this is the typical IS-LM result: monetary expansion lowers interest rates and raises output.

Finally, we have the case that may represent Japan with k < 1:

Monetary expansion leads to falling inflation, falling interest rates and falling output.  This is the neo-Fisherite result where inflation follows interest rates. Remember, this is output measured in money, not actual widgets. Also note that if we include nominal shocks, that puts a floor on the growth of n roughly equal to the growth of the labor force. If the labor force is growing at a rate of 1%, then n won't go below 1% on average (the same for 0% or -1%, as a shrinking labor force may be more relevant for some countries).

Those are cases I've talked about before (in much more confusing ways [1], [2]), but with the same basic results.

PS Here is the (very simple) code (onset of monetary expansion at t = 2, well, ii = 2). To get the other results, I used k = 1.1 and k = 0.9


  1. Seems very apropos for one of Krugman's blogs from today, about Japan. Question, then for you Jason- given that Japan is in an information trap, what do you as the hypothetical Tsar of information transfer economics advise the government of Japan to do to get inflation going in order to make some progress on the debt?

    1. Hi Todd,

      My prior probability on any theory is pretty low in this case -- but if I had to stick my neck out, I'd say an interest rate peg -- sell government bonds at a fixed interest rate. No open market prices; if you want a Treasury, you have to pay 99 cents for 1 dollar bond that pays in one year (a 1% interest rate). It may have worked in the UK, but it is too soon to tell ...

      It's in the links above. It may not matter what level the rate even is -- whether 0.375% for short rates and 2.5% for long rates in in the 1940s in the US or the 0.5% peg in the UK today.

      Not exactly sure what the mechanism is, though -- hence why I am unsure. Is it because it destroys the information carrying capacity of the interest rate markets? Does it fix us to a supply curve?

      No idea.

    2. Jason,

      Interestingly enough, mainstream economics provides an explanation for why an interest rate peg could help a country escape a liquidity trap (which is basically the mainstream economics version of the IT index is less than unity, as far as I can tell).

      In a liquidity trap, the money supply no longer determines the price level (see, e.g., Krugman's 1998 paper), so the only ways is can get off of the zero lower bound of its own volition is to contract the current money supply enough for the expected money supply to be high relative to the current money supply or to raise the expected money supply (this only works if the liquidity trap is expected to end at some point, which, because of the continuum of rational expectations equilibria, only occurs if the household randomly decides it will -- for some reason a lot of people don't properly understand that this decision is completely arbitrary; there is absolutely no reason for the household to choose any particular equilibrium). The treasury can alleviate this problem by using fiscal policy to force a higher interest rate without requiring the central bank to cause a recession by shrinking the money supply (by agreeing to sell however many bonds are demanded at a given interest rate). If the chosen interest rate is greater than zero (or the interest rate on reserves), then the price level is once again determined wholly by the central bank -- or, in ITM language, the IT index is greater than one -- and monetary policy can resume as normal.

    3. That is definitely interesting.

      The liquidity trap is less well-defined in the IT model, but yes, when the IT index k is close to or less than 1, you get less inflation response than you do when k is greater than 1.

  2. In no particular order (as a partial answer to my own question), my ideas would be:
    1. Print Yen, and helicopter drop it to Japanese consumers. By expanding M0 greatly, would you not then increase NGDP, and possibly redefine kappa? You mentioned in the past that places like Argentina and Brazil suffer from high inflation precisely because they print "too much" money.
    2. Peg the currency. As in a previous post, currency pegs in the past in other countries have been associated with elevated inflationary episodes, at times "hyperinflation". Perhaps a 3-5 year pegging of the Yen would be sufficient to ignite a good bout of inflation?
    3. Redefine the Yen. Make a "Yen Novo" worth 1/100 as much. Is it possible that this could then redefine the M0/NGDP ratio, making the kappa much lower, and thus producing a "developing" economy.

    What would be the advantages and disadvantages of each of these, both from an ITM and conventional economic point of view? Which would be best, in terms of minimizing potential downstream harm (e.g., a painful romp through a hyperinflationary episode)?

    1. Currency pegs work through open market operations -- you buy and sell currency on the open market in exchange for other currencies or other assets. You could set up a fixed exchange rate with a country with inflation, but for the US and Japan, that would probably just impact the other country.

      The treasury bond peg is different because you simply sell the bond at a single price in your own currency, like selling an iPhone in the US for 499 dollars (or whatever).

      Literal helicopter drops would potentially work ...

      Hyperinflation probably wouldn't be a problem ... a country like Japan or the US trying it would probably stop as soon as they saw large inflation and go back to the old policies.

    2. Since we're talking policy, what about issuing consols? IIUC, they do not add the government debt.

    3. So Japan should **literally** print money and spend it. Maybe give every adult 100000 Yen to spend right away, and use the rest to on big energy, infrastructure, and research projects. They should, as Krugman notes, be aiming for 4-5% annual inflation. Full employment+ money printing + big infrastructure/research projects could save Japan's economy, and allow them to inflate away the debt over time.

  3. Oops- point 3 above, the "Yen Novo" should be worth ~100 times as much (or 1000, or 10000, or ??)

  4. Nice piece, Jason. I'm not certain why debt levels (leverage) dont make much of an appearance in the literature. Interest rates are the price of debt. If zero rates cannot draw out nearly infinite leverage, then guess what: real economy balance sheets are tapped out. There's only so much oil underground.

    The debt stock is deflationary antimoney. For all of QE1's ferocity, it simply collateralized outstanding debt back to 1960s levels. The reserve collateral was already claimed, in a sense -- we were just waiting for the debt market to become overleveraged and receive a margin call. Then the central-bank-produced collateral appears, with no real-economy inflationary consequences. In fact, by preserving the notional value of debt, the deflationary impulses are neo-fisherite preserved.

    High debt economies have enormous excess reserves, low rates, and low inflation: Japan, Switzerland, the EU and US.


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